Ex 8.2,11
Prove that the coefficient of xn in the expansion of (1 + x)2n is twice the coefficient of xn in the expansion of (1 + x)2n–1 .
We know that
General term of (a + b)n is
Tr + 1 = nCr an – r . br
We have to prove
coefficient of xn in (1 + x)2n = 2 × Coefficient of xn in (1 + x)2n – 1
i.e. 2nCn = 2 × 2n-1Cn